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If P \neq NP then Some Strongly Noninvertible Functions are Invertible

Rabi, Rivest, and Sherman alter the standard notion of noninvertibility to a new notion they call strong noninvertibility, and show -- via explicit cryptographic protocols for secret-key agreement ([RS93,RS97] attribute this to Rivest and Sherman) and digital signatures [RS93,RS97] -- that strongly noninvertible functions would be very useful components in protocol design. Their definition of strong noninvertibility has a small twist (``respecting the argument given'') that is needed to ensure cryptographic usefulness. In this paper, we show that this small twist has a large, unexpected consequence: Unless P=NP, some strongly noninvertible functions are invertible.

preprint2000arXivOpen access
Lane A. HemaspaandraKari PasanenJörg Rothe
Computational Complexity
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Lane A. HemaspaandraKari PasanenJörg Rothe

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